P-Delta effect plus Time-History analysis or Response Spectrum analysis.

Dear Seniors:

 When I want to make a Time-History analysis or a Response Spectrum analysis is necessary to make a P-Delta analysis to include the second-order effect due the deformation of the structure produced by horizontal forces. STAAD is capable to make a P-Delta effect without any problem, but in its TECHNICAL REFERENCE says:

 “A PDELTA ANALYSIS will correctly reflect the secondary effects of a combination of load cases only if they are defined using the REPEAT LOAD specification... Secondary effects will not be evaluated correctly for LOAD COMBINATIONS”

But the REPEAT LOAD specification says:

“RESPONSE SPECTRUM LOAD and TIME HISTORY LOAD should not be used in REPEAT LOAD. It is also not available for loads generated using the program's load generation facilities such as UBC LOAD Generation, WIND LOAD Generation, MOVING LOAD Generation, etc”

My question is:

How I can to combine several loads case including Time History or Response Spectrum load case, or any other load derivate from generation load facility, to make an appropriate P Delta analysis?

It’s necessary to model the totality of the mass of the structure in the same directions to avoid that the mass be canceled. That's why is extremely necessary to "combine" it effect in one way (positive) and in the other way (negative) with the rest of the common load case like dead, live and others. How I can do that and reach an appropriate P Delta effect analysis?

I give you an example where I've defined a seismic load case using the response spectrum analysis, you can see the error that STAAD give me back because I use response spectrum in a repeat load specification.

25. LOAD 1 LOADTYPE DEAD TITLE Dead

26. SELFWEIGHT Y -1

27. MEMBER LOAD

28. 2 UNI GY -1.5

29. LOAD 2 LOADTYPE LIVE REDUCIBLE TITLE Live

30. MEMBER LOAD

31. 2 UNI GY -2

32. 2 CON GY -2 3

33. LOAD 3 LOADTYPE SEISMIC TITLE Seismic X

34. SELFWEIGHT X 1

35. SELFWEIGHT Y 1

36. MEMBER LOAD

37. 2 UNI GX 1.5

38. 2 UNI GY 1.5

39. 2 UNI GX 2

40. 2 UNI GY 2

41. 2 CON GX 2 3

42. 2 CON GY 2 3

43. SPECTRUM CQC IBC 2006 X 1 ACC DAMP 0.05 LIN

44. ZIP 92887 SITE CLASS B TL 8.000

45. LOAD 4 LOADTYPE NONE TITLE Repeat Load

46. REPEAT LOAD

47. 1 1.0 2 1.0 3 1.0 **ERROR- CASE BEING FACTORED IS DYNAMIC. CASE= 3

48. PDELTA KG 15 ANALYSIS SMALLDELTA PRINT MODE SHAPES

Parents
  • A better choice of input is as follows:

                                Ensure that you have requested enough modes. The default 6 is often not enough.

    CUT OFF MODES 20

    LOAD 1 LOADTYPE DEAD TITLE Dead
    SELFWEIGHT Y -1
    MEMBER LOAD
    2 UNI GY -1.5

    LOAD 2 LOADTYPE LIVE REDUCIBLE TITLE Live
    MEMBER LOAD
    2 UNI GY -2
    2 CON GY -2 3

                               Combine the static cases for PDELTA. For PDELTA the cases with both horizontal and vertical forces
                              will have more of the Pdelta effect.

    LOAD 4 LOADTYPE NONE TITLE Repeat Load
    REPEAT LOAD
    1 1.0 2 1.0

              To have the PDELTA effect in dynamic cases, place the case just before the PDELTA KG Analysis command.
              The dynamics will include the Kg matrix from the prior case (case 4).   | [K+Kg] - ω [M] | = 0

    LOAD 3 LOADTYPE SEISMIC TITLE Seismic X
    SELFWEIGHT X 1
    SELFWEIGHT Y 1
    MEMBER LOAD
    2 UNI GX 1.5
    2 UNI GY 1.5
    2 UNI GX 2
    2 UNI GY 2
    2 CON GX 2 3
    2 CON GY 2 3
    SPECTRUM CQC IBC 2006 X 1 ACC DAMP 0.05 LIN
    ZIP 92887 SITE CLASS B TL 8.000

                          Combine the static and dynamic by using the LOAD COMBINATION command.
                          Create two cases: static + dynamic and static - dynamic   since RSA dynamic results can be + or - .
                          If there are 2 or more dynamic cases, you should combine those dynamic cases with SRSS option in
                          LOAD COMBINATION.

    LOAD COMBINATION 5 LOADTYPE NONE TITLE LOAD COMB
    4 1.0 3 1.0

    LOAD COMBINATION 6 LOADTYPE NONE TITLE LOAD COMB
    4 1.0 3 -1.0

                           The PDELTA KG command does not need iteration value or smalldelta. They are included.

    PDELTA KG ANALYSIS
    PRINT MODE SHAPES

    Answer Verified By: Sye 

  • Hello RayC,

    The TECHNICAL REFERENCE states the same thing for the BUCKLING and DIRECT Analysis - namely:

    “A BUCKLING/DIRECT ANALYSIS will correctly reflect the secondary effects of a combination of load cases only if they are defined using the REPEAT LOAD specification... Secondary effects will not be evaluated correctly for LOAD COMBINATIONS”

    Does this workaround method that you described for the P-Delta work also for the two other types of analysis mentioned above?

    I would much appreciate if you could give me an answer at your earliest convenience!

    Kind Regards,

    Skerdi
  • Hello Sye,

    I have uploaded the two models in a zip file named "P-Delta Sensitivity Check".

    Thank you for your help.

    I am looking forward to hearing from you.
  • The reason for not seeing any difference between the analysis runs is that the time history analysis was being carried out twice in your models due to the manner in which the analysis commands were specified multiple number of times. For the second time, the dynamic case was being analyzed using a PERFORM ANALYSIS ( for the model With P-Delta ) which was not accounting for the KG when computing the stiffness. So essentially the results from both models were coming out same. Here is what you can do.

    In the file With P-Delta, make the following changes

    Remove the first PERFORM ANALYSIS and CHANGE after load case 13. This would not make a difference as far as end results are concerned but nevertheless the command is redundant.

    Move the PDELTA KG ANALYSIS and CHANGE from after load case 121 to a location after the load comb 17 as shown next

    LOAD COMB 17 1.0*(SW+DL)-1.0*BL
    4 1.0 121 -1.0
    PDELTA KG ANALYSIS
    *
    CHANGE

    Remove the PERFORM ANALYSIS PRINT ALL command from within the design block as shown next because this is redundant as well.
    …
    RATIO 0.9 MEMB 536 TO 583 696 TO 703 706 TO 709 718 719 732 733 784 TO 795
    LOAD LIST 14 TO 17
    PERFORM ANALYSIS PRINT ALL
    DEFINE ENVELOPE
    14 TO 17 ENVELOPE 1 TYPE STRESS
    …

    With these changes, rerun the analysis and you will see difference in results between two models for case 121 and for others involving those cases.



  • Hello Sye,

    Thank you for the quick reply. Therefore the changes would be:

    1. Move the PDELTA KG ANALYSIS and CHANGE from after load case 121 to a location after the load comb 17:

    LOAD COMB 17 1.0*(SW+DL)-1.0*BL

    4 1.0 121 -1.0

    *

    PDELTA KG ANALYSIS

    *

    CHANGE

    *

    PERFORM ANALYSIS       *Should I still keep this command?

     

    2. Remove the PERFORM ANALYSIS PRINT ALL command from within the design block:

    I am using a SELECT command on another identical model. I believe I should apply a PERFORM ANALYSIS command after the SELECT command so that Staad updates the results for the new sections. Does this contradict your advice to remove the PERFORM ANALYSIS command from the design block?

    It would look like this:

    . . .

    DFF 65 MEMB 696 TO 703
    DFF 65 MEMB 706 TO 709 718 719 732 733
    DFF 65 MEMB 536 TO 583 784 TO 795
    *
    RATIO 1.3 ALL
    RATIO 0.9 MEMB 536 TO 583 696 TO 703 706 TO 709 718 719 732 733 784 TO 795
    *

    *

    *** End of PARAMETER 1 - design check of the current sections

    *

    *

    SELECT MEMB 1 TO 99 101 TO 107 109 TO 115 117 TO 138 166 TO 192 200 TO 233 -
    241 TO 260 268 TO 335 358 TO 360 363 TO 365 368 TO 370 373 TO 375 -
    378 TO 380 383 TO 385 396 TO 410 421 TO 435 446 TO 460 471 TO 485 -
    496 TO 510 521 TO 535 584 TO 695 782 783
    GROUP AX MEMB 1 TO 84
    GROUP AX MEMB 85 TO 92 117 TO 138 322 TO 335 782 783
    GROUP AX MEMB _COL_INT
    GROUP AX MEMB _RAFT_EXT
    GROUP AX MEMB _RAFT_INT
    GROUP AX MEMB _TIE_B_FRONT_R
    GROUP AX MEMB _TIE_B_SIDE
    GROUP AX MEMB 696 TO 703
    GROUP AX MEMB 706 TO 709 718 719 732 733
    GROUP AX MEMB _ROOF-BEAMS
    GROUP AX MEMB 536 TO 583 784 TO 795
    *
    LOAD LIST 14 TO 17
    *

    *
    PERFORM ANALYSIS PRINT ALL

    *

    *

    *** Start of PARAMETER 2 - design check of the sections picked by SELECT command

    *

    **
    DEFINE ENVELOPE
    14 TO 17 ENVELOPE 1 TYPE STRESS
    END DEFINE ENVELOPE
    LOAD LIST 14 TO 17
    *
    PARAMETER 2
    CODE AISC UNIFIED
    METHOD ASD

    . . .

  • Andi, The answers to your queries are

    1. No. You do not need this PERFORM ANALYSIS

    2. If you need to reanalyze this model after selection, use the PDELTA KG instead of the PERFORM ANALYSIS



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